The buses were carrying almost 5,000 people from Foua and Kfraya, villages in northern Syria that have been besieged by rebels.
The buses had been waiting since late on Friday outside the city while the evacuation deal halted. The huge explosion earlier Saturday came as a much criticized population transfer deal stalled as the government and rebels bickered over who should be evacuated.
Residents from Kefraya and Foua were to be transferred government-controlled Jibrin, while those from Madaya and Zabadani were heading towards the rebel-held Idlib province.
The Britain-based Syrian Observatory for Human Rights said at least 24 people were killed.
Meanwhile, an Iraqi military statement said the Syrian air force has carried out a series of air strikes against Islamic State (IS) militants inside Syria, with one killing a leading member of the group in Raqqa, the IS de facto capital.
The explosion hit the Rashideen area, a rebel-controlled district outside Aleppo city where evacuation buses carrying almost 5,000 people from the northern rebel-besieged villages of Foua and Kfraya were stuck, causing a huge plume of black smoke.
The explosion took place at a transit point Rashideen area as thousands of evacuees from the regime-held, predominantly Shia towns of Foua and Kefraya waited on Saturday to continue their journey to regime-controlled Aleppo, the coastal province of Latakia, or Damascus, according to the Syrian Observatory for Human Rights. The Syrian government and rebels began a coordinated population transfer Friday of about 10,000 people from four towns besieged for years amid the country's bloody, six-year civil war.
State TV and an opposition monitoring group say the vehicle bomb left an undetermined number of people killed.
Syrian state TV blamed the rebels for obstructing the deal, causing thousands of evacuees to be stuck in bus depots overnight. A rebel official says at least 30 of his opposition fighters who were guarding the evacuees were killed in the blast.
Pro-opposition media also said that dozens were killed. Critics say the deal amounts to "demographic engineering". Al-Manar TV said the buses were to replace those damaged by the blast. "There's no drinking water or food".
An AFP correspondent, west of Aleppo speaking before the reports of an explosion, said coaches carrying government evacuees had not moved in 30 hours. "There was no other choice in the end - we were besieged inside a small area in Madaya". Assad is from the Alawite religious minority, often considered an offshoot of Shi'ite Islam.